Ab initio study of stability and quadrupole coupling constants in borophosphates.

The DFT method was used to predict the formation energies and quadrupole coupling constants C Q in a series of borophosphates: Li 3 BP 2 O 8 , Li 2 NaBP 2 O 8 , Na 3 BP 2 O 8 , Li 2 B 3 PO 8 , Na 5 B 2 P 3 O 13 , LiNa 2 B 5 P 2 O 14 and Na 3 B 6 PO 13 composed of different networks and different amounts of borate and phosphate units. The change in formation energies with increasing number of B atoms in this series is attributed to the multiplicity of boron sites and is explained by density of states calculations. The calculated C Q values of 7 Li, 23 Na and 11 B are correlated with the coordination and distortion of polyhedra to elucidate the influence of local and more distant environments. As for the C Q of 11 B, it should be in the ranges of 0.26-0.36, 0.48-0.84 and ∼1 MHz for boron tetrahedral distortion indices of 0.004-0.013, 0.015-0.019 and 0.033, respectively, whereas C Q ∼3.0 MHz corresponds to boron in a triangular site. The obtained numerical relationships make it possible to predict the quadrupole frequencies for these nuclei based only on their local environment, and vice versa , to propose structural models from NMR data. These results provide guidance for studying similar characteristics of other borophosphates, the structure of which varies depending on the initial reaction, composition and temperature.